The volume of a given mass of a gas at 17 deg C is 100 cm3. To what temperature should it be heatedunder the same pressure so that it would occupy a volume of 150 cm3?
Question
The volume of a given mass of a gas at 17 deg C is 100 cm3. To what temperature should it be heatedunder the same pressure so that it would occupy a volume of 150 cm3?
Solution
To solve this problem, we can use the combined gas law equation, which relates the initial and final volumes and temperatures of a gas under constant pressure. The equation is as follows:
(V1 / T1) = (V2 / T2)
Where: V1 = initial volume of the gas (100 cm3) T1 = initial temperature of the gas (17°C) V2 = final volume of the gas (150 cm3) T2 = final temperature of the gas (unknown)
Now, let's substitute the given values into the equation:
(100 cm3 / 17°C) = (150 cm3 / T2)
To find T2, we can cross-multiply and solve for T2:
100 cm3 * T2 = 17°C * 150 cm3
Dividing both sides by 100 cm3:
T2 = (17°C * 150 cm3) / 100 cm3
T2 = 25.5°C
Therefore, the gas should be heated to a temperature of 25.5°C under the same pressure in order to occupy a volume of 150 cm3.
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